The political turmoil in Ukraine is spreading. Protests that began last fall when the country's president refused to sign a trade deal with the European Union - under pressure from its neighbor Russia - have now moved out of the capital.

More disturbing for President Viktor Yanukovych, demonstrations are now occurring in cities normally supportive of his governing party. And they're all calling on Yanukovych to step down.

NPR's Corey Flintoff is on the line with us now from the capital, Kiev. Good morning.

COREY FLINTOFF, BYLINE: Good morning, Renee.

MONTAGNE: Let's start with how significant these reports of protests in other cities are. Sounds bad for the president.

FLINTOFF: Well, this could be very significant, Renee. Yanukovych's Party of Regions pretty much has dominated the industrial regions in the eastern and southern parts of this country. And up until now, there's been very little anti-government protest.

Now we're hearing that thousands of people have turned out in some big cities in the east and the south. They've tried to seize or block access to some of these regional government buildings, and they've clashed with police. We're hearing that there have been dozens of arrests.

You know, I talked with a number of people from the east and south at this protest camp here in Kiev, and they insist that there's a lot more people in their home towns that oppose Yanukovych, but up to now, they've been afraid to take action.

MONTAGNE: And the president offered what seemed to be pretty dramatic concessions over the weekend. He offered the post of prime minister to one of the main opposition leaders and the job of deputy prime minister to another. The opposition rejected that offer. Why?

FLINTOFF: Well, the opposition leaders say it's a trick, and it's something that would actually put them in a much worse position if they accepted it. Yanukovych would still hold power over the executive branch. His political party still controls the parliament. So they could basically make it impossible for the prime minister to accomplish anything. So I'd say this offer from Yanukovych has refocused the opposition on the original complaints that brought on this protest in the first place.

They're demanding an end to government corruption. They want the government to free political prisoners, and they want Ukraine to be aligned with the European Union, and not with Russia.

MONTAGNE: So, protesters have taken over government buildings. Where is that headed?

FLINTOFF: Well, it happened here in Kiev last night, protesters took over the Justice Ministry building. And Vitaly Klitschko - who is this former heavyweight boxing champion, I mean, he's emerged as one of the protest leaders - went to the ministry and tried to persuade these activists to leave, but they refused.

So, now the Justice Minister - she's a strong supporter of President Yanukovych - says that she'll ask him to impose a state of emergency if the protesters don't leave. And that, of course, would give the government a lot more wide-ranging authority to use force.

MONTAGNE: And, Corey, there have already been very violent protests. I mean, for the first time, last week several protesters were killed. A funeral for one of them drew thousands and thousands of people yesterday. Is there a risk that more extreme groups in the opposition are taking over?

FLINTOFF: Well, radicals and especially ultra-nationalists have been involved in some of the clashes that we've been seeing on TV, but, you know, I think it's clear, too, that the opposition leaders are having a really hard time controlling these people. But, you know, yesterday, at the funeral, I think I saw that the protest still has very solid middle-class support.

You know, the protest leaders had called for a big political rally in the main square, but they canceled it because of the funeral. And this demonstrator, he was a 25-year-old guy who was shot to death last week. And despite that, the square was filled up with tens of thousands of people, most of them just standing quietly.

And as I walked through that crowd, I was struck, you know, by the large numbers of women there, the large numbers of middle-class, middle-aged people who've been turning out week after week to oppose the government. So I think they still support the protest.

MONTAGNE: This would seem, Corey, like it's not ending any time soon. But what are the next steps, do you think?

FLINTOFF: Well, Yanukovych has called a special session of parliament for tomorrow, and he says it will act on some of these other concessions that he's offered. You know, for instance, he promised to change a recently passed law that would effectively ban most kinds of civic protest. In fact, it would ban most of the tactics that the opposition has been using for the past two months.

The opposition was outraged by the way that law was rammed through parliament, and they're saying they want it repealed, not changed. Yanukovych has also promised to come up with an amnesty for the protesters who've been arrested.

But, you know, now, it seems that if there's a way to resolve this peacefully, it's not going to come in the parliament. It's going to have to come in talks between the president and protest leaders.